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Modelling dependence in a ratemaking procedure with multivariate Poisson regression models

Author

Listed:
  • Lluís Bermúdez

    () (Departament de Matemµatica Econµomica, Financera i Actuarial, Universitat de Barcelona)

  • Dimitris Karlis

    () (Athens University of Economics and Business)

Abstract

When actuaries face with the problem of pricing an insurance contract that contains different types of coverage, such as a motor insurance or homeowner's insurance policy, they usually assume that types of claim are independent. However, this assumption may not be realistic: several studies have shown that there is a positive correlation between types of claim. Here we introduce di®erent multivariate Poisson regression models in order to relax the independence assumption, including zero-in°ated models to account for excess of zeros and overdispersion. These models have been largely ignored to date, mainly because of their computational di±culties. Bayesian inference based on MCMC helps to solve this problem (and also lets us derive, for several quantities of interest, posterior summaries to account for uncertainty). Finally, these models are applied to an automobile insurance claims database with three different types of claims. We analyse the consequences for pure and loaded premiums when the independence assumption is relaxed by using different multivariate Poisson regression models and their zero-inflated versions.

Suggested Citation

  • Lluís Bermúdez & Dimitris Karlis, 2010. "Modelling dependence in a ratemaking procedure with multivariate Poisson regression models," Working Papers XREAP2010-04, Xarxa de Referència en Economia Aplicada (XREAP), revised Apr 2010.
  • Handle: RePEc:xrp:wpaper:xreap2010-04
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    File URL: http://www.xreap.cat/RePEc/xrp/pdf/XREAP2010-4.pdf
    File Function: First version, 2010
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    File URL: http://www.xreap.cat/RePEc/xrp/pdf/XREAP2010-4.pdf
    File Function: Revised version, 2010
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    References listed on IDEAS

    as
    1. van Ophem, Hans, 1999. "A General Method To Estimate Correlated Discrete Random Variables," Econometric Theory, Cambridge University Press, vol. 15(02), pages 228-237, April.
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    More about this item

    Keywords

    Multivariate Poisson regression models; Zero-inflated models; Automobile insurance; MCMC inference; Gibbs sampling;

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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